Accelerated L_{1/ 2} regularization based SAR imaging via BCR and reduced Newton skills

Sparse synthetic aperture radar (SAR) imaging has been highlighted in recent studies. As an important sparsity constraint, L1_/2 regularizer has been substantiated effectively when applied to SAR imaging. However, L1_/2-SAR imaging suffers from a common challenge with other sparse SAR imaging methods: the computational complexity is costly, especially for high dimensional applications. This challenge is mainly due to that L1 _/2-SAR imaging is a gradient descent based method, of which the convergence is at most linear. Thus, a lot of iterations are often necessary to yield a satisfactory result. In this paper, we propose an accelerated L1 _/2-SAR imaging method by applying the block coordinate relaxation (BCR) scheme combined with the reduced Newton skill for acceleration. It is numerically shown that the proposed method keeps fast convergence within a very few iterations, and also maintains high reconstruction precision. We provide a series of simulations and two real SAR applications to demonstrate the superiority of the proposed method. Particularly, much faster convergence and higher reconstruction precision in imaging, of the proposed method over the other sparse SAR imaging methods.